Chess.com is down to the semifinals (12/13 and 12/16) of their Speed Chess Championships, finals 12/19. They will have live coverage.
https://www.chess.com/article/view/2021-speed-chess-championship-main-event#schedule
These are fun events, but a third of each match is "bullet chess" (1 minute time control with 1 second increment) which is too fast for me to follow. And they tend to be held during my work day.
The World Rapid and Blitz Championships (Kazakhstan) were recently postponed due to Covid, but have been rescheduled for Warsaw, Dec. 25-31.
https://en.chessbase.com/post/the-world-rapid-and-blitz-championships-will-take-place-in-warsaw
Carlsen is planning to compete. I will watch as much of these as possible, probably on chess24.com. There should be big showdowns between MC and Alireza Firouzja, who has been anointed as the probable next world champion.
Don't know about 2022 yet. But the big "Champions Chess Tour" of online tournaments will resume in February.
https://championschesstour.com/
These are great fun to watch, I expect chess24 will broadcast.